I would like it to run off the arduino power, Its uses a BT60 battery which according to http://www.dealextreme.com/details.dx/sku.23706 runs on 3.7V @ 1000mAh, however it has 4 pins and I have no idea how to use an arduino to act like its emulating this battery
since that is a lithium battery 2 of those pins are probably used to communicate battery charge information (so it doesnt explode), usually they are a 3 pin setup
I would take a multimeter to the battery and see which ones are putting out a voltage
okay well I found the 2 that give it power are the 2 outside ones at 3.7V, So im gunna guess my best bet is to just power the 2 outside pins of the phone with 3.7 V and ignore the 2 center ones?
it would be a starting place, what does the charger port look like, I assume its one of those funny multipin microscopic deals
ahh, I do like you're approach it looks like this 
Output: 5.00-6.00V/400mA
crap, Do you think it would still work at 300 mA?
well considering that some of it is for charging the battery ... maybe?
it would be best to power the phone with an amp meter wired in series with the + power line and see how much power this phone is asking for while doing various tasks